2.1, 2.3, 2.4 Inductive and Deductive Reasoning and Biconditional Statements

2.1, 2.3, 2.4
Inductive and Deductive Reasoning
and
Biconditional Statements

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Biconditional Statements
are definitions

In order for a TRUE bicondit= ional to be created, the conditional and converse of a statement must be TRUE.

Behold:

Conditional: If it is a square then it has four right angles = and four congruent sides.

Is this true?

Converse: If it has four right angles and four congruent = sides then it is a square.

Is this true?

Conditional: If it is a square then it has four right angles and four = congruent sides.

Since they are both TRUE, we= have = permission to write a biconditional.

Here’= s your rules:

1.Drop the ‘if’ and ‘then’.

2.Connect the hypothesis and = conclusion with ‘if and only if’.

Converse: If it has four right angles and four congruent sides then it is a square.

Let’s do it again…

If it is an equilateral trian= gle, then all of the side= s have the same measure.

If all the sides have the sa= me measure, then it is an equilateral triangle.

It is an equilateral triangl= e if and only if all of the sides have the same measure.

♥A biconditional is a definition.

♥ It can be read frontwards and backwards and be true.

♥ Notation: p q

♥ Abbreviation for ‘if and only if’ =3D iff

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Reasoning based on patterns you have observed.

1. How many sides does the fifth figure of Sequence A have?

2= . How ma= ny sides does the tenth figure of Sequence A have?

3= . How ma= ny sides does the fourteenth figure of Sequence A have? <= /span>

Find the pattern:

Figure #

# of sides

Figure # + 2 =3D # of sides

Generally, a guess based on past experience
(inductive reasoning)

If the hypothesis of a true conditional is true, then = the conclusion is true.

Let’s look in your book – pg 107.

Law of Syllogism:

Allows you to state a conclu= sion from two true conditional statements when the conclusi= on of one statement is the hypothes= is of the other statement.

Let’s look in your book – pg 108.

If p q is true

And p = ; is true

Then = ; q is true

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♥If the conditional and converse are tru= e, what do you have permission to make?

♥What is the notation for a biconditional statement?

♥Create a biconditional statement: If it is a line segment then it i= s a piece of a line with two endpoints.

♥What is inductive reasoning?

♥What is deductive reasoning?

♥What is the Law= of Detachment?

♥What is the Law of Syllogism?

♥What conclusion can you draw from the following statements? If it’s Monday, then it’s meatloaf. It’s Monday.=

♥What law does the previous statement demonstrate?

♥What conclusion can you draw from the following statements? If it’s ballet, then it’s beautiful. If it’s dan= cing, then it’s beautiful.

♥What law does the previous question demonstrate?

♥Your assignment ♥

pg. 109; 13-18, 20-27
pg. 118; 12-17

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